We derive the best predictive estimator (BPE) of the fixed parameters for a linear mixed model. This leads to a new prediction procedure called observed best prediction (OBP), which is different from the empirical best linear unbiased prediction (EBLUP). We show that BPE is more reasonable than the traditional estimators derived from estimation considerations, such as maximum likelihood (ML) and restricted maximum likelihood (REML), if the main interest is the prediction of the mixed effect. We show how the OBP can significantly outperform the EBLUP in terms of mean squared prediction error (MSPE) if the underlying model is misspecified. On the other hand, when the underlying model is correctly specified, the overall predictive performance of the OBP can be very similar to the EBLUP. The well known Fay-Herriot small area model is used as an illustration of the methodology. In addition, simulations and analysis of a data set on graft failure rates from kidney transplant operations will be used to show empirical performance. This is joint work with Jiming Jiang of UC-Davis and Thuan Nguyen of Oregon Health and Science University.
Groupe d’études et de recherche en analyse des décisions